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Rings in Network Glasses: The \(\mathrm{B_2O_3}\) Case

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Molecular Dynamics Simulations of Disordered Materials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 215))

Abstract

There has been a considerable debate, in particular since the emergence of atomistic simulations , about the structure of glassy \(\mathrm{B_2O_3}\) , a prototypical network-forming system based on trigonal units. Some intermediate-range order in the form of threefold rings, present in the glass but not in the crystalline phases, has remained so far very difficult to reproduce in atomistic simulations. After a brief summary of the evidences accumulated regarding the boroxol rings , a review of the numerical studies of liquid and glassy \(\mathrm{B_2O_3}\) is provided. The reasons for the failure of the quench-from-the-melt techniques are stressed and a methodology, based on first-principles calculations of experimental observables (diffraction, NMR, Raman, IR, heat capacity) from various glassy models is devised to provide incontrovertible answers to the debate. This allows assessing not only the content of boroxol rings but also the sensitivity of each observable to this quantity. The presence of threefold rings in the glass is then showed to have ramifications for the understanding of the crystalline and liquid phases. This includes the prediction of yet unknown \(\mathrm{B_2O_3}\) polymorphs structurally close to the glass, the understanding of the so-called crystallisation anomaly and the evidencing of structural transitions in the liquid . Finally, the discussion is extended to parent systems such as \(\mathrm{B_2S_3}\).

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Notes

  1. 1.

    Being related to a vibration of the oxygen atoms in the rings, the peak area is proportional to \(f_O\), which is directly related to \(f\), the number of boron atoms in the rings, by \(f = 1.5 f_O\).

  2. 2.

    The incorrect 32 % value quoted in [113] actually corresponds to \({f_\mathrm{at}}\) in [69] and thus to \({f}\) = 40 %.

  3. 3.

    Another source of errors in DFT-based calculations comes from the exchange-correlation functional used which is an approximation of the unknown exact one. Gradient-generalised approximation (GGA) based functionals, such as PBE [133] used here, tend to overestimate the equilibrium volume and thus lead to positive residual pressures in simulations at the experimental density. This problem is significantly reduced in some recently proposed functionals by the incorporation of van der Waals contributions. However, no systematic nor significant variation of \(\langle f \rangle \) (beyond the statistical error bars, \(\pm \)7 %) were observed in the liquid phase using the PBE-D2 [138] functional.

  4. 4.

    Although the liquid and glass densities are not identical, it may be a good enough approximation at this point.

  5. 5.

    As an alternative to the high-pressure synthesis, crystalline \(\mathrm{B_2O_3}\)-I can also be prepared by the stepwise dehydration of orthoboric acid (\(\mathrm{H_3BO_3}\))[164] or by seeding a melt with borophosphate [165].

  6. 6.

    As compared to [166], the calculations were repeated with tighter (more accurate) pseudo-potentials and a larger plane-wave basis-set cutoff of 784 eV. This resulted in some very small differences in the results shown Fig. 14.23.

  7. 7.

    If there are no relaxations at all in the triangle-boroxol substitution, that is for exactly homothetical \(3D\)-topologies, one expects the density ratio to be \(\frac{3}{2^3}=0.375\). This is close to the value obtained for instance in the T1 to T1-\(b\) case (0.35). However, the density ratio can be much higher because of structural relaxations, in particular in the directions orthogonal to the boroxol rings plane. For a topology with a strong lamellar character, the triangle-boroxol substitution will double the intra-layers lengths while keeping unchanged the inter-layer distance, resulting in this case in a density ratio of \(\frac{3}{2^2}=0.75\). This is indeed very close to the value obtained in the T0 to T0-\(b\) case (0.76). There are a few cases for which the density is unchanged (as in the T4 to T4-\(b\) case); these correspond to initially porous geometries which contain large rings and for which a more efficient packing in the final relaxed structure was achieved by folding the largest rings.

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Acknowledgments

I would like to thank all the co-workers involved in the [38, 78, 121, 136, 166, 200], in particular Francesco Mauri, Thibault Charpentier, Ari P. Seitsonen, Mathieu Salanne, Axelle Baroni and Matthieu Micoulaut. I also thank Pascal Richet for providing me with the experimental data of [156], François-Xavier Coudert for interesting discussions, Sara and Eva Lacarce for support and patience. Large support from the French supercomputers (GENCI-CINES/IDRIS) has made possible the results presented in this contribution (Grant x2014081875). I also acknowledge support from French state funds (managed by the ANR under reference ANR-11-IDEX-0004-02, cluster of Excellence MATISSE) and support from the HPC resources of The Institute for scientific Computing and Simulation (financed by Region \(\hat{\mathrm{I}}\)le de France and the project Equip@Meso under reference ANR-10-EQPX-29-01).

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  1. IMPMC, Université Pierre et Marie Curie, 4 Place Jussieu, 75005, Paris, France

    Guillaume Ferlat

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  1. IPCMS, Strasbourg University, Strasbourg, France

    Carlo Massobrio

  2. Dept. of Materials Science and Engineeri, University of North Texas, Denton, Texas, USA

    Jincheng Du

  3. Dept. of Materials Science, University of Milan Bicocca, Milan, Italy

    Marco Bernasconi

  4. Dept. of Physics, University of Bath, Bath, United Kingdom

    Philip S. Salmon

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Ferlat, G. (2015). Rings in Network Glasses: The \(\mathrm{B_2O_3}\) Case. In: Massobrio, C., Du, J., Bernasconi, M., Salmon, P. (eds) Molecular Dynamics Simulations of Disordered Materials. Springer Series in Materials Science, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-319-15675-0_14

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